Ocean Modeling I - CESM®

Ocean Modeling II

Parameterized Physics

Peter Gent

Oceanography Section

NCAR

PARAMETERIZATIONS IN CESM2 POP2

• Vertical mixing (momentum and tracers)- surface boundary layer - interior

• Lateral mixing: mesoscale eddies (tracers)

• Horizontal viscosity (momentum)

• Overflows

• Submesoscale eddies (tracers)

• Estuary box model parameterization

• Solar absorption

VERTICAL MIXING SCHEME:K-PROFILE PARAMETERIZATION (KPP)

• Unresolved turbulent vertical mixing due to small-scale overturning

motions parameterized as a vertical diffusion.

• Guided by study and observations of atmospheric boundary layer

where Kx represents an “eddy diffusivity” or “eddy viscosity”

and X = { active/passive scalars or momentum }

parameterize

1994


• KPP is not just a vertical diffusion scheme because the scalars

(Temp and Salinity) have non-local or “countergradient” terms γx

• KPP involves three high-level steps:

1. Determination of the boundary layer (BL) depth: d

2. Calculation of interior diffusivities: υx

3. Evaluation of boundary layer (BL) diffusivities: Kx

• Diffusivity throughout the boundary layer depends on the surface

forcing, the boundary layer depth, and the interior diffusivity.

• KPP produces quite large diffusivities below the boundary layer,

which mixes temp and salinity quite deep in times of very strong

surface wind stress, such as strong midlatitude atmosphere storms.


1. BL depth d is minimum depth where the bulk Richardson # (Rib)

referenced to the surface equals a critical Richardson # (Ricr=0.3).

Stabilizing buoyancy difference

Destabilizing velocity shear

Br : near-surface reference buoyancy

Vr : near-surface reference horizontal velocity

Vt(d) : velocity scale of (unresolved) turbulent shear at depth d

Ri measures the stability of stratified shear flow. “Boundary layer

eddies with mean velocity Vr and buoyancy Br should be able to

penetrate to the boundary layer depth, d, where they first become

stable relative to the local buoyancy and velocity.”

unresolved shear


2. Calculation of interior diffusivities

υx : interior diffusivity at depth d (below the boundary layer)

υxs : (unresolved) shear instability

υxw : internal wave breaking

υxd : double diffusion

υxc : local static instability (convection)

υxt : tidal mixing

Superposition of processes sets interior vertical diffusivity, υx,

below the surface boundary layer.

ux(d) =uxs(d)+ux

w(d)+uxd (d)+ux

c(d)+uxt (d)


Verification example at

Ocean Weather Station

Papa (50oN, 145oW):

Large et al (1994)

Lateral Mixing (Interior, Tracer Diffusion)

Mesoscale eddy mixing of tracers:Gent-McWilliams (GM) parameterization

1990

2011

GFDL climate model with ocean resolution of 0.1o

Lateral Mixing (Interior, Tracer Diffusion)

Why is GM needed?

O(1o) models do not resolve the 1st baroclinic deformation radius away

from the equatorial regions, and hence lack the mesoscale turbulence

which mixes temperature, salinity and passive tracers in the real ocean.

Agulhas Retroflection

ISOPYCNAL

(r=constant)

DEPTH

Ocean Observations suggest mixing along isopycnals

is ~107 times larger than across isopycnals.

• Early ocean models parameterized the stirring effects of (unresolved)

mesoscale eddies by Laplacian horizontal diffusion with KH = O(103 m2/s),

whereas the vertical mixing coefficient Kv = O(10-4 m2/s).

• Horizontal mixing results in excessive diapycnal mixing, which degrades the

ocean solution: e.g. Veronis (1975) showed that it produces spurious upwelling

in western boundary current regions which “short circuits” the N. Atlantic MOC.

• Thus, was a recognized need to orient tracer diffusion in z-coordinate models

along isopycnal surfaces, to be consistent with observed ocean mixing rates.

Why is GM needed?

Isopycnal slopes

are small O(10-3)

at most

The GM Parameterization

TTuut

T

2*).(

.0*.),/.(* uw z

GM (1990) proposed an eddy-induced velocity u* in addition to diffusion along isopycnal surfaces.

GM impacts

Gent et al. (JPO, 1995): Eddy-induced velocity (v*,w*)

acts to flatten isopycnals and minimize potential energy.

warm

cold

salty

fresh

light

dense

Temperature

Salinity

Temperature

Density

Salinity

time

Southern Hemisphere zonal wind jet

Baroclinic instability produces ACC eddies that try to flatten the

isopycnals and produce a MOC that opposes the mean flow MOC.

Southern Hemisphere zonal wind jet

Mean MOC

Eddy MOC

Baroclinic instability produces ACC eddies that try to flatten the

isopycnals and produce a MOC that opposes the mean flow MOC.

Danabasoglu et al. (1994, Science)

4o x 3o x 20L ocean model

Impacts of GM

(a) Horizontal Diffusion, MOC (u)

(b) GM, MOC (u)

(c) GM, MOC (u+u*)

Danabasoglu et al. (1994, Science)

4o x 3o x 20L ocean model

Impacts of GM

(a) Horizontal Diffusion

(b) GM

Deep Water Formation

In (b), deep water is formed

only in the Greenland/

Iceland/Norwegian Sea, the

Labrador Sea, the Weddell

Sea and the Ross Sea.

Mimics effects of unresolved mesoscale eddies as the sum of

- diffusive mixing of tracers along isopycnals (Redi 1982),

- an additional advection of tracers by the eddy-induced velocity u*

Scheme is adiabatic and therefore valid for the ocean interior.

Acts to flatten isopycnals, thereby reducing potential energy.

Eliminates any need for horizontal diffusion in z-coordinate OGCMs

eliminates Veronis effect.

Implementation of GM in ocean component was a major factor enabling

stable coupled climate model simulations without “flux adjustments”.

GM summary

Limerick 2004

There

There once was an ocean model called POP,

Which occasionally used to flop,

But eddy advection, and much less convection,

Turned it into the cream of the crop.

Ocean Modeling I - CESM®

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